Alternative architecture and control strategy july 2010 - joe beno

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  • Misc Data: Pulse Generator: 22MJ, 12,000RPM; ~1.5M ft-lbs torque; 5 pulses 3MW Gen: 15,000RPM; 8 salient pole synchronous machine
  • Alternative architecture and control strategy july 2010 - joe beno

    1. 1. An Alternative Architecture and Control Strategy for Hexapod Positioning Systems to Simplify Structural Design and Improve Accuracy <ul><li>Ground Based and Airborne Telescopes III Conference </li></ul><ul><li>July 2, 2010 </li></ul><ul><li>Dr. Joe Beno </li></ul><ul><li>University of Texas Center for Electromechanics </li></ul><ul><li>[email_address] ; (512)232-1619 </li></ul><ul><li>Co-authors: John Booth, UT-MDO & Jason Mock, UT-CEM </li></ul>
    2. 2. U niversity of Texas Center for Electromechanics <ul><li>CEM </li></ul><ul><ul><li>$12M-$18M industry and government sponsored R&D per year </li></ul></ul><ul><ul><li>Leading edge, applied, multi-disciplinary engineering </li></ul></ul><ul><ul><li>Emphasis on one-of-a-kind hardware demonstrations </li></ul></ul><ul><ul><li>~100 full time research staff </li></ul></ul><ul><ul><li>Core expertise in controlled actuation systems, energy conversion, actuator technology, and high performance electromechanical systems </li></ul></ul>Tracker Test Stand being Erected in CEM Lab CEM Machine Shop CEM High-Bay Lab Facility
    3. 3. Historical Context and Motivation <ul><li>Hexapods are common in modern telescopes – advantages of parallel vs. series positioning systems </li></ul><ul><li>Modern telescopes are optically faster so primary-secondary mirror alignment is more important than older telescopes </li></ul><ul><li>Hexapod payloads for modern telescopes are rapidly increasing --- HET Wide Field Upgrade increases hexapod payload by 7x </li></ul><ul><li>Typical result: </li></ul><ul><ul><li>Actuator: Drive screw and nut assembly; geared motor </li></ul></ul><ul><ul><li>Displacement Sensor: indirect measurement with rotary encoder on screw or motor shaft, influenced by actuator and mount compliance </li></ul></ul><ul><ul><li>Heavy, bulky actuator-sensor unit </li></ul></ul>Goal: Enable simple integration of direct linear sensors for better accuracy and reduce stiffness requirement (and mass) of actuators
    4. 4. Overview <ul><li>Conventional Design Approach </li></ul><ul><li>Optimize design & placement of 6 actuator-sensor units </li></ul><ul><li>High emphasis on actuator & mount stiffness </li></ul><ul><li>Alternative Design Approach </li></ul><ul><li>Decouple sensors from actuators </li></ul><ul><li>Actuator mission: apply force </li></ul><ul><li>Actuator length not needed for controls </li></ul><ul><li>Sensor defines hexapod </li></ul><ul><li>Sensor must be stiff, but carries no load </li></ul><ul><li>Added control sophistication </li></ul>Primary Application: Large, high precision, high accuracy hexapods with large payloads Force Actuator Displacement Sensor Lower Frame Upper Frame
    5. 5. Enabling Controls Approach
    6. 6. Controls Approach Overview <ul><li>Conventional Hexapod </li></ul><ul><ul><li>Determine desired hexapod leg lengths from desired pose of upper frame WRT to lower frame (simple geometry problem: “inverse kinematics solution”) </li></ul></ul><ul><ul><li>Use actuator’s imbedded sensor to estimate actual leg lengths </li></ul></ul><ul><ul><li>Use PID feedback controls determine actuator forces necessary to drive leg length error toward 0 </li></ul></ul><ul><ul><li>(Why not do position control to directly drive error to zero?) </li></ul></ul><ul><li>But for any set of leg-lengths there are up to 40 different mathematically possible upper frame orientations (not all physically possible). </li></ul><ul><li>. . . PID controller “selects” closest possible solution . </li></ul>
    7. 7. Controls Approach Overview <ul><li>Decoupled Sensor Hexapod </li></ul><ul><ul><li>Think of sensors as Virtual Actuators </li></ul></ul><ul><ul><li>Determine desired virtual leg lengths from desired pose of upper frame WRT to lower frame (simple inverse kinematics problem) </li></ul></ul><ul><ul><li>Use sensors to determine length of Virtual Actuators </li></ul></ul><ul><ul><li>Use PID feedback controls to determine Virtual Actuator forces necessary to drive virtual leg length error toward 0 </li></ul></ul><ul><ul><li>Determine actual pose of upper frame from sensor values (“forward kinematics” problem – more to follow) </li></ul></ul><ul><ul><li>Use actual pose of upper frame to determine line of action of actual actuators (length of actual actuators not needed) </li></ul></ul><ul><ul><li>Determine force required from real actuators to apply same net force and moment on upper frame as Virtual Actuator would apply </li></ul></ul>
    8. 8. Forward Kinematics Solution <ul><li>Totally general hexapods: </li></ul><ul><ul><li>6 unknown degrees of freedom; 6 known leg lengths </li></ul></ul><ul><ul><li>Analytical solution not yet known, but there are 40 solutions (not all physically possible) for any given set of leg lengths. </li></ul></ul><ul><ul><li>Numerical solutions not accurate enough </li></ul></ul><ul><li>Approach: </li></ul><ul><ul><li>Identify hexapod leg configuration that can be solved analytically ( A n =  B n ) </li></ul></ul><ul><ul><li>Deploy sensors (virtual actuators) according to identified configuration </li></ul></ul><ul><ul><li>Deploy real actuators in any other convenient, stable nonsingular configuration </li></ul></ul>
    9. 9. Forward Kinematics Solution ( A n =  B n ) Force Actuator Displacement Sensor Lower Frame Upper Frame
    10. 10. Forward Kinematics Solution Set #1 of 3 equations in 3 unknowns Ji & Wu 2001 Set #2 of 3 equations in 3 unknowns
    11. 11. Forward Kinematics Solution <ul><li>Solve for rotation matrix first; most foolproof approach: </li></ul><ul><li>Choose Type I Euler Angle Sequence (example rotate  about X axis;  about new Z axis;  about new Y axis) </li></ul><ul><li>R = [ c  c  -c  s  c  + s  s  c  s  s  + s  c  </li></ul><ul><li>s  c  c  -c  s  -s  c  s  s  c  + c  s  -s  s  s  + c  c  ] </li></ul><ul><li>where s=sin, c=cos </li></ul>
    12. 12. Forward Kinematics Solution <ul><li>Solve for rotation matrix first; most foolproof approach: </li></ul><ul><li>Choose Type I Euler Angle Sequence (example rotate  about X axis;  about new Z axis;  about new Y axis) </li></ul><ul><li>R = [ c  c  -c  s  c  + s  s  c  s  s  + s  c  </li></ul><ul><li>s  c  c  -c  s  -s  c  s  s  c  + c  s  -s  s  s  + c  c  ] </li></ul><ul><li>where s=sin, c=cos </li></ul><ul><li>Start with Equation Set #2 </li></ul>Terms picked out by Eqn Set #2
    13. 13. Forward Kinematics Solution <ul><li>Solve for rotation matrix first; most foolproof approach: </li></ul><ul><li>Choose Type I Euler Angle Sequence (example rotate  about X axis;  about new Z axis;  about new Y axis) </li></ul><ul><li>R = [ c  c  -c  s  c  + s  s  c  s  s  + s  c  </li></ul><ul><li>s  c  c  -c  s  -s  c  s  s  c  + c  s  -s  s  s  + c  c  ] </li></ul><ul><li>where s=sin, c=cos </li></ul><ul><li>Start with Equation Set #2. Use sin = sqrt (1- cos 2 ) to get three equations with cos(  ), cos (  ), and cos (  ) as three unknowns. Turn the crank with an algebraic solver (e.g., MATLAB or Maple). </li></ul><ul><li>Move to Equation set #1, use substitution and turn the crank to solve for P(x,y,z). </li></ul>Terms picked out by Eqn Set #2
    14. 14. Forward Kinematics Solution <ul><li>Result: </li></ul><ul><li>Solved with one-time 6x6 matrix inversion; one 6x6 matrix-vector multiplication and ~ 20 analytical expressions </li></ul><ul><li>8 solutions, typically ~ half are real: Pick solution closest to desired– assumes hexapod in good control </li></ul><ul><ul><li>(same assumption made with conventional hexapod when PID controller gravitates toward one solution) </li></ul></ul>
    15. 15. Determine Real Actuator Force <ul><li>Sum of Moments on Upper Frame from Virtual Actuators = Sum of Moments on Upper Frame from Real Actuators </li></ul><ul><li>Sum of Forces on Upper Frame from Virtual Actuators = Sum of Forces on Upper Frame from Real Actuators </li></ul><ul><li>Result: 6 linear equations, solved with one 6x6 matrix inversion </li></ul>
    16. 16. Sensor Considerations <ul><li>Precision external linear sensors and custom mounting system </li></ul><ul><ul><li>Absolute position feedback </li></ul></ul><ul><ul><li>Micron accuracy and sub-micron resolution </li></ul></ul><ul><ul><li>High-stiffness sensor mount </li></ul></ul><ul><ul><li>Appropriate degrees of freedom in the integration and mounting scheme </li></ul></ul><ul><ul><li>Housed in telescoping tube with linear bearings to ensure alignment of read head </li></ul></ul><ul><ul><li>Attached to hexapod frames with degrees of freedom typical of hexapod actuators, but much smaller because of negligible loads </li></ul></ul>Sensor example: Heidenhain LC 183
    17. 17. Benefits <ul><li>Weight Savings: Preliminary assessment: </li></ul><ul><li>50% actuator weight reduction: </li></ul><ul><ul><li>Base actuator design on material survival limits (no yield, fatigue life, etc.) </li></ul></ul><ul><ul><li>Stiffness just adequate to allow actuator to act as two-force member </li></ul></ul><ul><li>25% actuator weight reduction: </li></ul><ul><ul><li>Material limits same as above </li></ul></ul><ul><ul><li>Stiffness requirement half that of conventional stiff actuator-sensor design approach </li></ul></ul><ul><li>Additional Design Freedom: actuators and actuator configuration </li></ul><ul><li>Retrofits: May allow inexpensive upgrade to existing hexapods that do not meet desired performance needs – add sensor set </li></ul>

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